This is an updated version of a story first published on Nov. 1, 2024 For centuries, students have learned that in a right triangle, the square of the hypotenuse equals the sum of the squares of the ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved the ...

For ages, countless mathematicians have advanced mathematics through proofs. This is because proof is a key tool for developing new theories and solving problems. That’s why a discussion about proofs ...

For centuries, the Pythagorean Theorem has occupied a unique position in mathematics: both elementary and profound. Its equation, a² + b² = c², is taught early and used widely, yet its implications ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future. In May, a ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...

Ananyo Bhattacharya is chief science writer at the London Institute for Mathematical Sciences and the author of The Man from the Future: The Visionary Ideas of John von Neumann. One of the biggest ...